The main motivation of this paper is to introduce the notion of cubic linear space. This inspiration is received from the structure of cubic sets. The notions of R-intersection, R-union, P-intersection, and P-union of cubic linear spaces are defined and we provide some results on these. We further introduce the notion of internal cubic linear space and external cubic linear space and establish some results on them.
This paper is an inspiration received from the hybrid structures of metric space and group theory in fuzzy setting namely fuzzy metric group. As a generalization of this structure in intuitionistic fuzzy setting we introduce the notion of intuitionistic fuzzy 2-metric group (IF 2-MG) and study some properties on it.
In this paper we introduce the notion of anti fuzzy M-semigroup, inspired by the theory of M-semigroup and fuzzy M-semigroup . We justify that the intersection of two anti fuzzy M-semigroup is again an anti fuzzy M-semigroup and the union need not be true by means of a counter example. Given two anti fuzzy M-semigroup we define the generalized Cartesian product of two anti fuzzy M-semigroup and provide some interesting results on it.
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